Okay this may be a little longer post BUT I am trying to explain the details and if someone can tell me what to do greatly appreciated.

I have a 2 story house and 2 full bathrooms
Entry Level: Shower/Bath Tub-Sink -Toilet
Lower Level:Shower only -Sink-Toilet
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1 day ago it was very cold outside and so I let my kitchen sink drip water so pipes wouldn't freeze. My son shut off the dripping water in the kitchen sink, I didn't know until I got home from work. So I proceeded to go into the kitchen and turn the water on nothing came out at first. No hot or cold water. So I went and turned on all the other water supplies -sinks and after a few minutes the water was back to normal water came out fine. So I proceeded to let it drip again.
Well yesterday I went to take a shower before I go to work and I went to turn the shower on which is one handle circle shaped base plate that turns counter clockwise and goes from cold to hot if that makes sense.
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So upon turning the handle to have the water come out I turn the handle and the cold water is only dripping and as long as I turn the handle further down so it reaches hot it is fine. Hot water flows just not cold water.
Now prior to that day the shower worked fine.
I checked all the other faucets in the house- they are all fine and flowing hot or cold even the lower lvl shower is fine both hot and cold works fine.

It is just the cold side of the shower/bathtub entry lvl that isn't working properly and only dripping cold but free flowing hot.
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Can someone explain to me what to do next. I have tried turning all faucets on and leave them running and leaving the shower downstairs running for about 10 minutes straight. That didn't fix it. I looked at the water heater which is less than 3 months old and no leaks nothing. Someone said there might be something stuck in the line but it worked a few days ago and only started having issues upon it being cold.
I even thought maybe draining the water heater not sure. Thanks in advance Shan-

It sounds like you have a anti scald faucet and the balancing spool is stuck. A cartridge replacement will solve your problem. If it's a Delta or Moen faucet a call to there 800# will get you a new cartridge shipped to you free of charge.

I agree with John, likely a cartridge. However just out of curiosity what make makes you scared the lines will freeze? Has it happened before or are they ran on an outside wall? You shouldn't have to leave taps dripping to prevent them from freezing. Where I live it dips below 0 farenheit for a least 4-5 weeks a year and if your plumbing is run properly you have nothing to worry about.

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If you don't learn something new everyday at work, it's not even worth going.

Well first off no pipes are near the walls and/or outside all running away from walls so I just assumed you had to drip water. 2nd The cartridge thing is for the kind of fixture I have? Just making sure. I have a cheap (most likely) American Standard T375.248 Single Handle Tub and Shower Valve Trim with Metal Lever Handle, FloWise Single Function Showerhead and Diverter Tub Spout
So that is what I have, But even more like in the post 1st thing was I turned kitchen faucets on and nothing came up for a few minutes until I am guessing opening the other sinks up and then it worked fine. So if it is this cartridge thing I see 2 screws on the base plate just take them off and I am pretty sure either get it at home depot or even 26.00 and get a new one correct?

Ok well that's good, you should be good to go. I wouldn't worry about running water if it gets cold out. It'll just wind up costing you extra. As long as you keep your house at a reasonable temperature when your away. Now that's odd that there was no water pressure at first and the taps. First things first you need to have the water off to the house or isolate the shower. Post some pics of the valve. Personally never replaced an American standard shower valve, but usually there's a set screw to remove the handle, then remove the cover plate (typically two screws) and then post a pic, or if your able to figure it out then that great. American standard I believe has a lifetime warranty so if you want a free one you can probably call them and they should send you one. Worst case scenario, pull the cartridge out and go to Home Depot and get the replacement (if they carry them I'm not totally sure) sometimes if I have two people ill have the cartridge out, turn the water on for a few seconds and make sure you have water pressure at the valve, and it can flush any debris out. When your turn the water off be sure to open taps upstairs and down to drain the lines. Ideally if you can get the right cartridge before you replace then there's less down time. Let us know how it goes and feel free to ask any more questions and we will help the best we can!

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If you don't learn something new everyday at work, it's not even worth going.

I did a search for that model #. I couldn't find a schematic that showed how to remove that valve cartridge, but I do recall that style to be pretty self explanatory once you get the handle and chrome cover tube off.

There appears to be a cover plate on the face of the handle that you just pry out. Then a screw under that needs to be removed. The cover tube will pull off by hand, then you should be able to see how to proceed from there.